Topology Seminar: From elementary abelian p-group actions to p-DG modules

A basic open problem in equivariant topology is to determine lower bounds for the sum of mod-p Betti numbers of finite CW-complexes with a free (Z/p)^n-action. For p=2, Carlsson connected chain complexes with a free (Z/p)^n-action to DG modules over a polynomial ring in order to establish lower bounds using commutative algebra.

In joint work with Jeremiah Heller, we extend this connection to all primes using p-DG modules as developed in the Hopfological algebra framework by Khovanov and Qi. In this talk, I will provide an introduction to Hopfological algebra and explain its relevance for our work.